This is an excellent and well-written article. I think a good example of an incredibly compelling villain is Darth Vader, of the Star Wars saga. Throughout the story, he is shown to be capable of horrific acts, such as overseeing the destruction of an entire planet, as well as personally killing incompetent subordinates without a second thought.
Yet, as the story progresses, the audience absolutely cannot help but feel sympathy for him. As we find out that he is the protagonist's father, we also start to see that he is deeply conflicted, even tortured, over his own evil actions. The tension between his loyalty to his master and his desire to protect his son drives his conflict, and makes him seem all the more real, despite the fact that he can choke people with his mind. Darth Vader is truly one of the great villains of any narrative.